Crop Insurance

Lecture XXXI

Valuing Crop Yield Insurance

The general concept of insurance is the construction of an instrument or gamble that pays the purchaser in the event of some adverse occurrence.

Frequently purchased insurance contracts include life insurance that pays in the event of the holders death, car insurance that pays in the case of an accident, catastrophic health insurance that pays in the event of a major medical event such as cancer, etc.

Under commercial insurance arrangements the premium charged for the insurance is generally considered to be actuarially sound. Specifically, the expected indemnity payments are exactly equal to premiums charged.

Each of these contracts specifies a payable event, an indemnity (the amount to be paid on the event), and a premium (the amount paid for insurance contract). If the premiums exceeded the expected indemnity

payments then insurance firms would earn abnormal profits. These abnormal profits would be bid out of the market by new firms entering the insurance arena.

If premiums fell short of the expected indemnity, the insurance firm would loose money and ultimately exit the industry.

The actuarial value of an insurance contract can then be written as

V is the value of crop yield insurance P is the price of the crop y is the variable of integration f(y) is the probability density function for crop yields y* is is the minimum insured yield (trigger yield in crop

insurance).

*

0

)(y

dyyfyPV

Current debates in the area of crop yield insurance involve: Estimation of the probability density function for

yields f(y).Most common statistical applications assume that the

probability density function is normal or asymptotically normal. This assumption may have serious shortcomings in the

valuation of crop insurance.

From an agronomic perspective, yields are bounded by zero on the downside and limiting nutrients such as nitrogen on the up side. Hence, at the least, the x (-,) of the normal would appear

to be violated However, the truncated normal distribution may be

appropriate for crop yields.

The debate of potential normality of crop yields typically revolves around skewness and kurtosis. Skewness is a measure of nonsymmetry of the

distribution. The normal distribution is symmetric and, hence, yields

zero skewness. A significant portion of the literature supports skewness

in yields, but as pointed out by Just and Weninger, it does not reach a consensus on the direction of skewness.

Kurtosis measures the relationship between the area in the tails and the area around the means.

The second area of debate in the area of crop insurance is the moral hazard/incentive compatibility dimension of crop insurance.

A basic problem in any insurance contract is the determination of the insurable event and the amount of damages.

A second problem is the difficulty of self-selection. Specifically, as in health insurance contracts, riskier farmers will be willing to pay more money for insurance than safer farmers.

Valuing crop yield insurance. Using the data from Ramirez, Moss and

Boggess, we derive the parameters of the normal distribution function for corn as =173.03, =8.71.

*

0

2

88.151

03.173exp

271.8

1y

yyPV

Insurance and Coverage

Level of Insurance Cost of Premium

.90 * 173.03 10.73

.85 * 173.03 .63

.80 * 173.03 .01

Integrating Price Insurance

In order to integrate price risk the actuarial premium becomes

* *

0 0

),(p y

dpdypyfypV

The joint distribution is specified using the futures price as an efficient estimate of the price at harvest time. The price at harvest time can be estimated as a

function of the futures price at planting:

th

tht fp 110

Given traditional assumptions, 0 is the

anticipated basis and 1 is equal to one. The

distribution of price is then a function of the distribution of t.